Use the data sets found in Appendix C to answer this exercise. Is the proportion of race laps Terri completes slower than $130$ seconds less than the proportion of practice laps she completes slower than $135$ seconds?

Given in the question that, Use the data sets found in Appendix C to answer this exercise. we need to find that whether the proportion of race laps Terri completes slower than $130$ seconds less than the proportion of practice laps she completes slower than $135$ seconds.

a. The null hypothesis is $H_0:p_1\ge p_2$

b. Alternate hypothesis

$H_a:p_1>{p_2}^{}$

c. The random variable is the percentage of race laps completed in less than $130$seconds vs practise laps completed in less than $135$seconds.

d. Student's$t$distribution.

e. Fill in all requirements using Minitab's two sample$t$test option.

The result will be

Test results statistics $4.58$

f. The output has a $p$-value of $0.00$.

g. The graph of the $p$value is unnecessary because the value is $0.00$.

i. $\alpha =0.05$

ii. Decision: the null hypothesis will not be rejected.

iii. Justification for Decision: $p-$value>$\alpha$

iv. Final Thoughts: At the $5\%$level of significance, there is insufficient evidence to establish that the proportion of race laps completed in less than $130$seconds is fewer than the proportion of practise laps completed in less than135seconds.